Now showing items 1-6 of 6

    • An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Springer, 2022)   Artículo / Artikulua  OpenAccess
      We derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three ...
    • A convergent and asymptotic Laplace method for integrals 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Elsevier, 2023)   Artículo / Artikulua  OpenAccess
      Watson’s lemma and Laplace’s method provide asymptotic expansions of Laplace integrals F (z) := ∫ ∞ 0 e −zf (t) g(t)dt for large values of the parameter z. They are useful tools in the asymptotic approximation of ...
    • New analytic representations of the hypergeometric functions p+1Fp 

      López García, José Luis Upna Orcid; Palacios Herrero, Pablo Upna Orcid; Pagola Martínez, Pedro Jesús Upna (Springer, 2021)   Artículo / Artikulua  OpenAccess
      The power series expansions of the hypergeometric functions p+1Fp (a,b1,…,bp;c1,…,cp;z) converge either inside the unit disk |z|<1 or outside this disk |z|>1. Nørlund’s expansion in powers of z/(z−1) converges in the ...
    • Series representations of the Volterra function and the Fransén–Robinson constant 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Elsevier, 2021)   Artículo / Artikulua
      The Volterra function μ(t,β,α) was introduced by Vito Volterra in 1916 as the solution to certain integral equations with a logarithmic kernel. Despite the large number of applications of the Volterra function, the only ...
    • Uniform approximations of the first symmetric elliptic integral in terms of elementary functions 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Springer, 2022)   Artículo / Artikulua  OpenAccess
      We consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y ...
    • Uniform convergent expansions of integral transforms 

      López García, José Luis Upna Orcid; Palacios Herrero, Pablo Upna Orcid; Pagola Martínez, Pedro Jesús Upna (American Mathematical Society, 2021)   Artículo / Artikulua  OpenAccess
      Several convergent expansions are available for most of the special functions of the mathematical physics, as well as some asymptotic expansions [NIST Handbook of Mathematical Functions, 2010]. Usually, both type of ...

      El Repositorio ha recibido la ayuda de la Fundación Española para la Ciencia y la Tecnología para la realización de actividades en el ámbito del fomento de la investigación científica de excelencia, en la Línea 2. Repositorios institucionales (convocatoria 2020-2021).
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